Project Summary Positron Emission Tomography (PET) can be used to assess physiological or pathological processes via the use of specific tracers. Acquisition time of a clinical or research PET scan can vary from minutes to hours, depending on the application. During the acquisition, patients breathe and may undergo voluntary body motion. Both respiratory motion and body motion may cause artifacts or tracer quantification error in the reconstructed images. Many motion correction methods have been proposed in the past, for either respiratory motion or body motion. However, there has been no unified approach that can simultaneously correct for both motions. Lack of full correction for both motions can result in inadequate correction results. In addition, to detect motions, external devices are commonly used in research studies. Device-based methods typically require attachments to the patient, which is not clinically accepted. Instead, data-driven methods, based on the PET raw count data to detect motions, are clinically attractive. However, for data-driven methods, the presence of body motion can impair the detection of respiratory motion (cross-talk effect), which can result in sub-optimal correction performance. In this study, we propose to develop algorithms to correct both body and respiratory motions, simultaneously for PET/CT. Specifically, we will devise a data-driven method which handles the motion cross- talk effect, to accurately detect both body and respiratory motions. Finally, our approach will be applicable to both single-bed and whole-body PET. The proposed algorithms will be first validated, evaluated and optimized using 4D PET simulations with multiple tracers and simulated respiratory and body motions, based on human measurements. In vivo validation will be performed using previously acquired non-human primate data. CT scans before- and after- motion positions will be used as the gold standard for comparison. Existing datasets of human dynamic PET studies with several tracers will be used to test the proposed algorithms. Both semi- quantitative metrics and absolute quantitative metrics will be used to test the efficacy of the proposed algorithms. Successful development of these algorithms will lead to retrospective and prospective evaluation in larger trials in the future. With GPU acceleration, the motion estimation process of proposal is very computationally efficient. In addition, with the GPU acceleration development of the list-mode reconstruction in the future, the computation time of our proposed method will be fully clinically acceptable.